Question

a string is wrapped several times around a solid cylinder and the end of string is held stationary while the cylinder is released from rest with no initial motion. Thenthe acceleration of the cylinder and the tension in the string will be

Answer 1

Let the mass of cylinder is m and radius of it is r.

so, moment of inertia of cylinder , I = 1/2 mr²

torque = moment of inertia × angular acceleration

force × displacement = 1/2 mr² × (a/r)

we know, linear acceleration, a = r × angular acceleration

T × r = 1/2 mr × a

T = 1/2 ma ......(1)

now, net force = ma

weight - tension = ma

or, mg - 1/2 ma = ma

or, mg = 3/2 ma

or, a = 2g/3

hence, tension in the string =1/2 ma = mg/3 and acceleration = 2g/3

Answer 2

Answer:

the answer is 2 g÷ 3 .........